Simplify the following expression: $r = \dfrac{-30n}{10n - 50}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-30n = - (2\cdot3\cdot5 \cdot n)$ The denominator can be factored: $10n - 50 = (2\cdot5 \cdot n) - (2\cdot5\cdot5)$ The greatest common factor of all the terms is $10$ Factoring out $10$ gives us: $r = \dfrac{(10)(-3n)}{(10)(n - 5)}$ Dividing both the numerator and denominator by $10$ gives: $r = \dfrac{-3n}{n - 5}$